Question
How is
obtained from ![left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent](data:image/png;base64,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)
The correct answer is: You could also get the value of from by just multiplying a with .
ANSWER:
Hint:
, where
is called the binomial expansion of
.
We are asked to find how
can be obtained from
.
Step 1 of 1:
The binomial expansion of
![left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent equals to the power of n minus 1 end exponent C subscript 0 x to the power of n minus 1 end exponent y to the power of 0 plus to the power of n minus 1 end exponent C subscript 1 x to the power of n minus 2 end exponent y to the power of 1 plus to the power of n minus 1 end exponent C subscript 2 x to the power of n minus 3 end exponent y squared plus horizontal ellipsis plus to the power of n minus 1 end exponent C subscript n minus 2 end subscript x to the power of 1 y to the power of n minus 2 end exponent plus to the power of n minus 1 end exponent C subscript n minus 1 end subscript x to the power of 0 y to the power of n minus 1 end exponent](data:image/png;base64,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)
Multiply then expansion by
, that is:
![left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent left parenthesis x plus y right parenthesis equals left parenthesis x plus y right parenthesis open parentheses blank to the power of n minus 1 end exponent C subscript 0 x to the power of n minus 1 end exponent y to the power of 0 plus to the power of n minus 1 end exponent C subscript 1 x to the power of n minus 2 end exponent y to the power of 1 plus to the power of n minus 1 end exponent C subscript 2 x to the power of n minus 3 end exponent y squared plus horizontal ellipsis plus to the power of n minus 1 end exponent C subscript n minus 2 end subscript x to the power of 1 y to the power of n minus 2 end exponent plus to the power of n minus 1 end exponent C subscript n minus 1 end subscript x to the power of 0 y to the power of n minus 1 end exponent close parentheses](data:image/png;base64,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)
![left parenthesis x plus y right parenthesis to the power of n minus 1 plus 1 end exponent equals x open parentheses blank to the power of n minus 1 end exponent C subscript 0 x to the power of n minus 1 end exponent y to the power of 0 plus to the power of n minus 1 end exponent C subscript 1 x to the power of n minus 2 end exponent y to the power of 1 plus to the power of n minus 1 end exponent C subscript 2 x to the power of n minus 3 end exponent y squared plus horizontal ellipsis plus plus to the power of n minus 1 end exponent C subscript n minus 2 end subscript x to the power of 1 y to the power of n minus 2 end exponent plus to the power of n minus 1 end exponent C subscript n minus 1 end subscript x to the power of 0 y to the power of n minus 1 end exponent close parentheses](data:image/png;base64,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)
![plus y open parentheses blank to the power of n minus 1 end exponent C subscript 0 x to the power of n minus 1 end exponent y to the power of 0 plus to the power of n minus 1 end exponent C subscript 1 x to the power of n minus 2 end exponent y to the power of 1 plus to the power of n minus 1 end exponent C subscript 2 x to the power of n minus 3 end exponent y squared plus horizontal ellipsis plus to the power of n minus 1 end exponent C subscript n minus 2 end subscript x to the power of 1 y to the power of n minus 2 end exponent plus to the power of n minus 1 end exponent C subscript n minus 1 end subscript x to the power of 0 y to the power of n minus 1 end exponent close parentheses](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAskAAAAVCAYAAAC0VnOQAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAABptJREFUeNrtXd+HXUccH1dFVIWKihVV1or7EBWqIqpWiaq1om8VtarCijzUfQjRh+hDlKrqQ6y8VEVElYpaK6JU1IrqS8SqqipR/QeiVsW6Qjpf53u4Ob33nNk735n5zpzPhy977t27e77z+dyZz8yZH8bEwzUb7xsdOGbjso0d0w9I5Ltq4w+O1Z7lnguecoxt/GxjqWdl1leuKd+3E+qlL0C7UU4dh/IMD62eYRYPazY2Ut3UNb4BLbhpY52/bH2Ab76nbGzbOMzxE7/Wh9xzxMDGBRsPelZmfeSaMLTxd0K99AVoN8qp41CeYaHZM7TxsMZ+NXpv4juPz9e9kPvce7wk3CvVBo35btpYnrh+08ZWT3LPlWvCnuIyA9eyhuGRAr2gHi0TT5XyEFKz0I8fpDxDCh5umcgj3zs80jFv5f+Enf9RGyeEGgOtYtWa7y7f2+R97vYk91y5XuaevMYyA9dy+dIoDT0i/FCBXlCPwiTnVsdBP2Eg4RlS8TA0EafEvO4p4pPcg6jxho27M5KdFb5iXbTxORfaY1M91rxi48UA5aUhX9fPjQvMvRSuF0w1X29RaWUOrmXyrd/zncompRct6Ju+tJrkHOo46CeeZsYZ8bDN/jU4aHL0xx6fP2vjRuP6esQv/0Ubt031qKDuFb1sYyR8H1ryde0VPmfkR5LBtcz/OcZ5LCge8QDXcv/nkI1PTTXHLrVetKBv+tJqknOo46CfMJDwDCl5IN/6SYwG8nsbKx6fv2rjfOP6XKRCorkvX0UWVsp829CcX7TMX2LJ/wmu/fOlRuMOG6cUegHXafIl7EXWS4pHxtBXXiZZWx0H/cSDj2fQwMMK+1cvQX1t470pr494ZIPwl40jgiZ709N0u+ZIPdWH3PuRABH72ZTXrzRIT5GvC4+0KpVWp9KjnpdM9ShiRbhiAtf++VLjMfT8zsYwyeBaNl8acbo/B9ddesnVJJeirxBw1axEu5GijoN+dOinyzOk0o+rHhbYv3oJ6gNTzZmZxPM2/jTVYhICzaUZeCRBk7QPtlz7FE7b3JUvmCxJPGh0GGihzYaCfF14JKzya3RPHwWomMC1f75dubpyvd+5XeA6Hdc0gvyDjVfm4HpenrWb5JL0FQIumpVoN1LUcdCPHv20eYZU+nHV0ID9q5egyNE3t3ajORyXE1ekEvjdyG9S/o6NL/nn02b6BPQUcOExRsMGrsE1uAbX0Fd4SGg2tL6gH+gnNcYu7rrNbZPb/23imobUHzacfo4meWDC7b34o6nm5uyYZ0fuUsKFR99e2rw9f3ANrsF1f7mGvsLBV7PS+jLQD/SjTD9jF4F1YXI4mnoWoynvD0xeOGDkd26oMeKCf1VZzl08ltp7B9fgGlznw3Vf9aVVsyH1Bf1AP6k7LY8lBHXPVPv5LXIvoGmIfRfupcK/ppof4wqXM8ppj79bLIazyvLt4rHUimkermed+w6uy+K6HmmihoD2Y10C1zDJwnVJiPKJqdmQ+oJ+0iBm+6ZZP0eMwMI9Au1hd8bGN2b6hva+W8ClAq28vOj4uy5nlJMItvgL8IKpVqIfVpRvF48lV0z74ZrQdu47uC6L63pE4YKpFquAa5hkaX2FQCzNhtQX9JMGMds3zfoR2QKOMGJif53xvu9hIqlAK8Uf8b3XJ9zQXJlVzvf0xO92nVFOc23umP/vFHFTUb5dPJZcMe2H6668wHWZXBP2wPVcXDfnfnZd90lf9ZNHMho0+ntJ+H5CazakvvpokjXpJ0b7plk/ToeJuOBdLswzM95/zVRD6jliiXs6u5zjP6Z6xNAcGW87o/wA90aOTvn735pqlagGdPFYOly5bqtEwHW5XFMneBtcz93YSpnkkvRF7cQTNhikoxNskKQQQ7N9r0tK1k+M9k2zfu6xf/UGJfdLx+/QI59hwaKWOKM8NVx4BPIalQDXMqBN5Wl+5yK4BgRx0jx7AAzN87zb0snYz84MsTQLfZWpn1jtm1b9kF/dkfpjNPR+quN36BHBVsFilTijPDVceATKMMng2h20iOU2mw5wDUiCFjzdaFxfz0yz0Fd5+onZvmnVD/nVtyT+0HHjfhY3nSSzXqhYJc4oT4njmd0vTDK4joEFrsQPZXr/4Fo3rto437g+l5Fmoa/y9BOzfdOqn3X2q8lIXStQrF1nlAMwyUB+ILMxRDEAgdDc+WlToN2AZqEftG/zg/zpBqQVBm1nlAPlmWOtpzYB4BnIA9RWHGy5hmaB2PqBhqbgPwZWFbiWIwAQAAAFDnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4rPC9tbz48bWk+eTwvbWk+PG1mZW5jZWQgc2VwYXJhdG9ycz0ifCI+PG1yb3c+PG1zdXA+PG1yb3cvPjxtcm93PjxtaT5uPC9taT48bW8+JiN4MjIxMjs8L21vPjxtbj4xPC9tbj48L21yb3c+PC9tc3VwPjxtc3ViPjxtaT5DPC9taT48bW4+MDwvbW4+PC9tc3ViPjxtc3VwPjxtaT54PC9taT48bXJvdz48bWk+bjwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTwvbW4+PC9tcm93PjwvbXN1cD48bXN1cD48bWk+eTwvbWk+PG1uPjA8L21uPjwvbXN1cD48bXN1cD48bW8+KzwvbW8+PG1yb3c+PG1pPm48L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjE8L21uPjwvbXJvdz48L21zdXA+PG1zdWI+PG1pPkM8L21pPjxtbj4xPC9tbj48L21zdWI+PG1zdXA+PG1pPng8L21pPjxtcm93PjxtaT5uPC9taT48bW8+JiN4MjIxMjs8L21vPjxtbj4yPC9tbj48L21yb3c+PC9tc3VwPjxtc3VwPjxtaT55PC9taT48bW4+MTwvbW4+PC9tc3VwPjxtc3VwPjxtbz4rPC9tbz48bXJvdz48bWk+bjwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTwvbW4+PC9tcm93PjwvbXN1cD48bXN1Yj48bWk+QzwvbWk+PG1uPjI8L21uPjwvbXN1Yj48bXN1cD48bWk+eDwvbWk+PG1yb3c+PG1pPm48L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjM8L21uPjwvbXJvdz48L21zdXA+PG1zdXA+PG1pPnk8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPis8L21vPjxtbz4mI3gyMDI2OzwvbW8+PG1zdXA+PG1vPis8L21vPjxtcm93PjxtaT5uPC9taT48bW8+JiN4MjIxMjs8L21vPjxtbj4xPC9tbj48L21yb3c+PC9tc3VwPjxtc3ViPjxtaT5DPC9taT48bXJvdz48bWk+bjwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bW4+MjwvbW4+PC9tcm93PjwvbXN1Yj48bXN1cD48bWk+eDwvbWk+PG1uPjE8L21uPjwvbXN1cD48bXN1cD48bWk+eTwvbWk+PG1yb3c+PG1pPm48L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjI8L21uPjwvbXJvdz48L21zdXA+PG1zdXA+PG1vPis8L21vPjxtcm93PjxtaT5uPC9taT48bW8+JiN4MjIxMjs8L21vPjxtbj4xPC9tbj48L21yb3c+PC9tc3VwPjxtc3ViPjxtaT5DPC9taT48bXJvdz48bWk+bjwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTwvbW4+PC9tcm93PjwvbXN1Yj48bXN1cD48bWk+eDwvbWk+PG1uPjA8L21uPjwvbXN1cD48bXN1cD48bWk+eTwvbWk+PG1yb3c+PG1pPm48L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjE8L21uPjwvbXJvdz48L21zdXA+PC9tcm93PjwvbWZlbmNlZD48L21hdGg+AE3+zAAAAABJRU5ErkJggg==)
![left parenthesis x plus y right parenthesis to the power of n equals open parentheses blank to the power of n minus 1 end exponent C subscript 0 x to the power of n y to the power of 0 plus to the power of n minus 1 end exponent C subscript 1 x to the power of n minus 1 end exponent y to the power of 1 plus to the power of n minus 1 end exponent C subscript 2 x to the power of n minus 2 end exponent y squared plus horizontal ellipsis plus to the power of n minus 1 end exponent C subscript n minus 2 end subscript x squared y to the power of n minus 2 end exponent plus to the power of n minus 1 end exponent C subscript n minus 1 end subscript x to the power of 1 y to the power of n minus 1 end exponent close parentheses plus](data:image/png;base64,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)
![open parentheses blank to the power of n minus 1 end exponent C subscript 0 x to the power of n minus 1 end exponent y to the power of 1 plus to the power of n minus 1 end exponent C subscript 1 x to the power of n minus 2 end exponent y squared plus to the power of n minus 1 end exponent C subscript 2 x to the power of n minus 3 end exponent y cubed plus horizontal ellipsis plus to the power of n minus 1 end exponent C subscript n minus 2 end subscript x to the power of 1 y to the power of n minus 1 end exponent plus to the power of n minus 1 end exponent C subscript n minus 1 end subscript x to the power of 0 y to the power of n close parentheses](data:image/png;base64,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)
Note:
You could also get the value of
from
by just multiplying a
with
.
Related Questions to study
Use Pascal triangle to expand (x + y)6
The expansion of the polynomial (x + y)6 can be found using the values of 6Cr
Use Pascal triangle to expand (x + y)6
The expansion of the polynomial (x + y)6 can be found using the values of 6Cr
Use polynomial identities to multiply the expressions ?
![open parentheses 25 straight x squared minus 15 straight y squared close parentheses open parentheses 25 straight x squared plus 15 straight y squared close parentheses](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![open parentheses 25 straight x squared minus 15 straight y squared close parentheses open parentheses 25 straight x squared plus 15 straight y squared close parentheses](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![12 cubed plus 2 cubed](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![12 cubed plus 2 cubed](data:image/png;base64,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)
Use Pascal triangle to expand ![left parenthesis x plus y right parenthesis to the power of 5](data:image/png;base64,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)
The answer cam also be found by expanding the formula of 5Cr .
Use Pascal triangle to expand ![left parenthesis x plus y right parenthesis to the power of 5](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADcAAAASCAYAAAD/ukbDAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAPUJuPDwAAAaBJREFUeNpjYBj64D8WjBVkAXHHIPVEB9R92DxHEOgB8fFBHktHoe4k2XMgjQaD3HPGQHwYi+d+AfEFII7HpskA6rmhAA5DPYkMmKBie4E4Fl1DFxDn0DDDUxPk4SkXhIH4CrrgDiC2xaI4GYdBzVA5anpuLhCHYxEvAOJWJL4lNIawATYgvoUu+AkqgQ2cA2JxJH4iEE+hQczFQ1MQMuCCOlYYzQOfsOjngwYQRr77g8dSDyDug7Jd8IQapZ7zAuJVaGL1QFyLRe0vNPP/QEv6SGwG/yFg8W4gtoeWSMJkVKrEVLLo+UUUiO8CMQcBzxEE+JIlLN3/wlLHULtA+YbE7oPaiy1ffSLFAaCYscYhBxJfA7UsksaeAxXzSlB8F1rEowNLUrMGrqoAZMkmaMbmAeIzRCRLSjy3EIj9gHgptvoKCnKwFDx4AbZKHJTmt6F5xgeIF9PQcwXQEu8SiZU4QXAcKU+B0vU6IJbGom45tASlBQiABoYfCc0vosBgaDj7EXDDUTILNTDIGOAuzzZogYGrXEgbqp1OHSDeQk0DAXAUZOWOXYrsAAAAiHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4oPC9tbz48bWk+eDwvbWk+PG1vPis8L21vPjxtaT55PC9taT48bXN1cD48bW8+KTwvbW8+PG1uPjU8L21uPjwvbXN1cD48L21hdGg+rS+pUgAAAABJRU5ErkJggg==)
The answer cam also be found by expanding the formula of 5Cr .
Use polynomial identities to multiply the expressions ?
![open parentheses 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y close parentheses](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![open parentheses 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y close parentheses](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKoAAAATCAYAAAAAs5Y/AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAsRJREFUeNrtmt9HZkEYx0dWstaSZKWLJUkXeUVXyUp0sdZ6ZUm6SFastV7r/QfSRZbsRfaim73Yi7XWktVF8ookySuRJCuJtf9DF0mW2e8cz8sYM+fMeTtn3jPtPHx5z3vmzDzzmV/PzDmMuTVOuoXqUD8LFpgW2Nqgd9BJQBGYNmOioisOy7u5B8xWiFtg6ohpCTp06Mw4tH9PBnid+AWm+TONbgxL1xNQDbqmUXoJfYK6MnCih8rrc1DhlxTD5Wkj0EFgmj/TYaqkbHvQK6hdSbd9RwcGoC0Cm7c9gs4dQGUEdSQwzZUp+whVLB++uuOoFzPKY0fLx2dowRHU90os6gNT7hnTaEQ/s3hQLCsXmv8XDBuGZbrXMAF00FEnHYN2ExrExu8v0IwmTRX6IF2PSuX5wpR7xjQa0e0xDj6BXlNM9cKQ5oTSNUykX9OAUZWHibqcQU8tGiTJ73maHWV7SCy6lDKvPGPKPWPK/sZURFY1xrnn0Cr9nlRHQguONyqWDZLkt+hE68p/S9CiJq9bz5hyz5gaoTasE5qCjugIxGQ7dP80g50stxAzHAnVUzZInN/i+pd03Q39hjqa7KiBafNME5cpecd3FHO/ShmXWjibCv/6U0JN8vta+r1qmAXTLv1FYMo9Yxr1/jFLp29iAu2fVOhsCztq2hnDxu8D2vT00chv06RRA38fmHLPmFofpZQo4NXtXDcpIBYzxDHL5hA77wax9fsrVIa+Q3OGvCrKBsEHptwzptrDafEqbhp6QL1dvFX5Qzs2psQXNcUZ8ebiW8E7ahq/q3SkchZThs2Bf9GYcs+YRnaoxBPiDHCLliWhPSpUjSE2oF5NIT9o91fEjprW7ynKo2zI3/QKNTDNnqnzDyh8snICm6J8lPI/MI3sLXP7SZovVqPAXmcihnoT82xgmj3TYBobouU6WAuZ/gOiK0S6F0rrxwAAAUp0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bXJvdz48bW4+MzwvbW4+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPiYjeDIyMTI7PC9tbz48bW4+NDwvbW4+PG1pPng8L21pPjxtaT55PC9taT48L21yb3c+PC9tZmVuY2VkPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93Pjxtbj4zPC9tbj48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1uPjQ8L21uPjxtaT54PC9taT48bWk+eTwvbWk+PC9tcm93PjwvbWZlbmNlZD48L21hdGg+SVC8UAAAAABJRU5ErkJggg==)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![27 x to the power of 9 minus 343 y to the power of 6](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![27 x to the power of 9 minus 343 y to the power of 6](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 10 plus 21 right parenthesis squared](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 10 plus 21 right parenthesis squared](data:image/png;base64,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)
How is ( x + y )n obtained from (x + y)n-1
You could also get the value of from
by just multiplying a ( x + y) with
.
How is ( x + y )n obtained from (x + y)n-1
You could also get the value of from
by just multiplying a ( x + y) with
.
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![m to the power of 8 minus 9 n to the power of 10](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![m to the power of 8 minus 9 n to the power of 10](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 7 plus 9 right parenthesis squared](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 7 plus 9 right parenthesis squared](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ? 123 + 23
This can also be done by finding the cube of each values and adding them. But that might be time consuming. Hence, we use these identities.
How can you use polynomial identities to factor polynomials and simplify numerical expressions ? 123 + 23
This can also be done by finding the cube of each values and adding them. But that might be time consuming. Hence, we use these identities.
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![open parentheses 11 cubed close parentheses plus 5 cubed](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![open parentheses 11 cubed close parentheses plus 5 cubed](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ? ![27 x to the power of 9 minus 343 y to the power of 6](data:image/png;base64,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)
We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.
How can you use polynomial identities to factor polynomials and simplify numerical expressions ? ![27 x to the power of 9 minus 343 y to the power of 6](data:image/png;base64,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)
We use identities to speed up the process of multiplication and simplification. There are some basic polynomial identities that you need to by heart.